1. In ABC and XZW, m A = m X and m B = m Z 1. In ABC and XZW, m A = m X and m B = m Z. What can you conclude about m C and m W? ANSWER They are the same. 2. Solve = . x 18 54 9 ANSWER 108 3. ABC DEF. Find x. ~ ANSWER 10

Show that triangles are similar. Use the AA Similarity Postulate. Target Show that triangles are similar. You will… Use the AA Similarity Postulate. .

Vocabulary AA Similarity Postulate 22 – If two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar. Similarity statement

EXAMPLE 1 Use the AA Similarity Postulate Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. SOLUTION Because they are both right angles, D and G are congruent. By the Triangle Sum Theorem, 26° + 90° + m E = 180°, so m E = 64°. Therefore, E and H are congruent. Similarity statement ANSWER So, ∆CDE ~ ∆KGH by the AA Similarity Postulate.

EXAMPLE 2 Show that triangles are similar Show that the two triangles are similar. a. ∆ABE and ∆ACD SOLUTION Because m ABE and m C both equal 52°, ABE C. By the Reflexive Property, A A. So, ∆ ABE ~ ∆ ACD by the AA Similarity Postulate.

X X EXAMPLE 2 Show that triangles are similar Show that the two triangles are similar. b. ∆SVR and ∆UVT X X SOLUTION You know SVR UVT by the Vertical Angles Congruence Theorem. The diagram shows RS ||UT so S U by the Alternate Interior Angles Theorem. So, ∆SVR ~ ∆UVT by the AA Similarity Postulate. Are they similar if the sides are not parallel? No

GUIDED PRACTICE for Examples 1 and 2 Show that the triangles are similar. Write a similarity statement. 1. ∆FGH and ∆RQS In each triangle all three angles measure 60°, so by the AA similarity postulate, the triangles are similar; ∆FGH ~ ∆QRS. ANSWER

GUIDED PRACTICE for Examples 1 and 2 Show that the triangles are similar. Write a similarity statement. 2. ∆CDF and ∆DEF Since m CDF = 58° by the Triangle Sum Theorem and m DFE = 90° by the Linear Pair Postulate the two triangles are similar by the AA Similarity Postulate; ∆CDF ~ ∆DEF. ANSWER

Standardized Test Practice EXAMPLE 3 Standardized Test Practice SOLUTION x ft 64 in. 50 ft 40 in. = 40x = 64(50) x = 80 ------- 64 in. The flagpole is 80 feet tall. The correct answer is C.

GUIDED PRACTICE for Example 3 4. What If ? A child who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow? 58 in. ANSWER 36.25 in. ------- 64 in. 5. You are standing in your backyard, and you measure the lengths of the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree. tree height your height = length of your shadow length of tree shadow